It is worth noticing that when \(f(\cdot )\)  is differentiable, then \(\nabla f(x) \in \partial _C f(x)\)  and if \(f(\cdot )\)  is continuously differentiable or strictly differentiable, then \(\partial _C f(x) =\lbrace \nabla f(x)\rbrace \) .
Now, we are ready to explain the notion of Clarke Jacobian sign-stability through the following definition, which is a generalization of Jacobian sign-stability in [1]} ( cf. Corollary REF ).
